Markov Processes on Curves for Automatic Speech Recognition

We investigate a probabilistic framework for automatic speech recognition based on the intrinsic geometric properties of curves. In particular, we analyze the setting in which two variables-one continuous (), one discrete (s)-evolve jointly in time. We sup(cid:173) pose that the vector traces out a smooth multidimensional curve and that the variable s evolves stochastically as a function of the arc length traversed along this curve. Since arc length does not depend on the rate at which a curve is traversed, this gives rise to a family of Markov processes whose predictions, Pr[sl ]' are invariant to nonlinear warpings of time. We describe the use of such models, known as Markov processes on curves (MPCs), for automatic speech recognition, where are acoustic feature trajec(cid:173) tories and s are phonetic transcriptions.